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Math Help - High School Maths problem Sum

  1. #1
    Junior Member
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    High School Maths problem Sum

    Hi Guys,

    I am stuck with this High school maths problem sum which is killing me !

    My tutor dosen't allow me to use algebra to solve this question =(


    Here goes the question :

    Alex bought some fishes and dogs for $96. He bought 3 times as many dogs as fishes. He paid $30 more for the fishes than the dogs. Each fish cost $10.40 more than each dog.

    a)How many Fishes did he buy?

    b)What is the cost of each dog?


    Any kind soul pls help !

    This question is killing me !
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: High School Maths problem Sum

    You have 4 equations is 4 unknowns. Let F = number of fish, D = number of dogs, Pf = price of a fish, Pd = price of a dog:

    Quote Originally Posted by liukawa View Post
    Alex bought some fishes and dogs for $96.
    F(Pf) +D(Pd) = 96

    Quote Originally Posted by liukawa View Post
    He bought 3 times as many dogs as fishes.
    D = 3F

    Quote Originally Posted by liukawa View Post
    He paid $30 more for the fishes than the dogs.
    F x Pf = 30 +D(Pd)

    Quote Originally Posted by liukawa View Post
    Each fish cost $10.40 more than each dog.
    Pf=10.40 +Pd

    Now to work through these four equations:

    1. Put the value for D from equation 2 into equation 1. This reduces the problem to 3 equations in 3 unknowns:

    F(Pf) + 3F(Pf) = 96
    F(Pf) = 30 +3F(Pd)
    Pf=10.4+Pd

    2. Put the value for Pf from the third equation into the first two:
    F(10.4+Pd) + 3F(Pd) = 96
    F(10.4 + Pd) = 30 + 3F(Pd)

    3. Subtract the 2nd equation from the first:
    3F(Pd) = 96-(30+ 3F(Pd)); so F xPd = 11

    4. Put F(Pd) =11 into the first equation:
    10.40 F + 11 +3(11) = 96

    Which yields F = 5

    Now you can back substitue this into the previous equations to get the values for Pd, Pf, and D.
    Last edited by ebaines; July 13th 2012 at 08:43 AM.
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  3. #3
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    Re: High School Maths problem Sum

    You should be able to use whatever method you want. I see solutions involving less algebra (e.g. no system of equations) but eventually you'll have to use at least a little algebra, unless you're plainly guessing and checking.
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